2 edition of Some results of uniqueness and existence of constrained matrix problems. found in the catalog.
Some results of uniqueness and existence of constrained matrix problems.
Thesis (Ph.D.)- Univ. of Birmingham, Dept of National Economic Planning, 1974.
 and want to prove the existence of multiple solutions for variational problems. The Connection Lemma is a slightly different version of the Mountain Pass Lemma, which is usually ex- plained in terms of paths connecting points a and b which have f(a) and f(b) below a critical level c. existence and uniqueness of a solution is proved in [13, Theorem 2] assuming that det(H(Y)) 6= 0, where H(Y) is a matrix functional de ning boundary conditions, and Y is a d-solution, a solution of the system that satis es only the interface conditions. This condition is hard .
By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function. The theorems obtained are very Cited by: 2. The theorems improve the generality and applicability of standard uniqueness and existence results in the theory of viscosity solutions. AB - Uniqueness and existence theorems are established under the Osgood type condition for viscosity solutions of the Cauchy problem for fully nonlinear degenerate parabolic partial differential equations of Cited by: 8.
ON THE EXISTENCE AND UNIQUENESS OF THE REAL LOGARITHM OF A MATRIX WALTER J. CULVER1 1. Introduction. Consider the exponential matrix equation () C = e* where C is a given real matrix of dimension nX«. What we shall examine in this paper are the conditions under which a real matrix X exists to satisfy () and, obtaining existence, the. A research on the existence and uniqueness result for certain nonlinear boundary value problems of capillarity problem has a close relationship with practical problems. Some significant work has been done on this, see Wei et al [1, 5, 2, 4, 3, 7, 10, 6]. In , Wei Author: C. L. Ejikeme, M. B. Okofu.
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In this paper, some uniqueness and existence results for the solutions of the initial-boundary-value problems for the generalized time-fractional diffusion equation over an open bounded domain G × (0, T), G ⊂ R n are given. To establish the uniqueness of the solution, a maximum principle for the generalized time-fractional diffusion equation is by: A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text.
Some theoretical results about second-order work, uniqueness, existence and controllability independent of the constitutive equation Chapter December with 12 Reads How we measure 'reads'Author: René Chambon.
generalized critical points under some regularity assumptions. In this paper, we present further generalization and applications of our results in two recent network control mod-els. We restrict ourselves to \box-constrained " regions and establish uniqueness of the generalized critical point under weaker regularity assumptions.
The Existence and Uniqueness Theorem for Linear Systems OCW SC Let x 1(t) and x 2(t) be two solutions to (1) on the interval I, such that at some point t 0 in I, the vectors x 1(t 0) and x 2(t 0) are linearly independent.
Then a) the solutions x 1(t) and x 2(t) are linearly independent on I, and b) the vectors x 1(t 1) and x 2(t 1) are linearly independent at every point. existence and uniqueness of solutions of the linear sparse matrix problem considered.
Keywords: banach fixed point theorem, contraction mapping, sparse matrix. Introduction and Preliminaries The Banach fixed point theorem was introduced by Stefan Banach in [1, 2]. The theorem is an important tool in the theory of metric spaces in. It turns out that existence and uniqueness theorems for (simple, linear) model equations are often the cornerstone for proving existence results of more complicated equations like nonlinear equations.
You can often view a nonlinear elliptic PDE as a differentiable map between Banach manifolds, the derivative of which is then a linear PDE.
under suitable assumptions the existence and uniqueness of a solution is proved. As a consequence, a condition to guarantee the existence of at least one periodic solution for a class of Li´enard equations is presented. Key Words and Phrases: Nonlinear boundary. just to mention some.
Very recently some basic theory for the initial value problems of fractional differential equations involving Riemann-Liouville differential operator has been discussed by Lakshmikantham and Vatsala [12,13].
Some existence results were given for the problem (1)-(2) with q 1 by [1 4 ] and q 1, 1D by Tisdell in [19 ]. You can prove existence and uniqueness by using the properties given without using the determinant.
In fact, this is now one can prove that the function determinant exists without really writing the formula. $\endgroup$ – Beni Bogosel Jun 16 '15 at We study periodic solutions for nonlinear second-order ordinary differential problem. By constructing upper and lower boundaries and using Leray-Schauder degree theory, we present a result about the existence and uniqueness of a periodic solution for second-order ordinary differential equations with some by: 2.
In this paper we study a class of nonlinear parabolic problems with \(p(x,t)\) growth conditions. We prove the existence and uniqueness of bounded solutions to such a problem, with less constraint to \(p(x,t)\).Our results are generalizations of the corresponding results in Cited by: 4.
The Existence and Uniqueness (of the solution of a second order linear equation initial value problem) A sibling theorem of the first order linear equation Existence and Uniqueness Theorem Theorem: Consider the initial value problem y″ + p(t) y′ + q(t) y = g(t), y(t0) = y0, y′(t0) = y′ Size: KB.
Existence and Uniqueness Results for Some Nonlinear Boundary Value ProblemsCited by: The Lasso Problem and Uniqueness Ryan J. Tibshirani Carnegie Mellon University Abstract The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n.
But when p > n, the lasso criterion is not strictly convex, and hence it may not have a unique minimizer. these results, Section 5 focus on establishing some existence, uniqueness and ap-proximation results on Lp solutions of BSDEs with Lp (p>1) data (Section ) and RBSDEs with Lp (p>1) data (Section ) under weaker assumptions, which answers those questions put forward before.
We note that the work of this paper (even for Theorems on non Author: ShengJun Fan. of Sections 3 and 4, we obtain existence, uniqueness, and comparison results for the IBVP (). Special cases and examples axe given in Section 5 to illustrate the obtained results.
Finally, in Section 6, we study problems where the initial condition (# • u')'(to) = c2 is replaced by the. necessity of some of the hypotheses in the existence and uniqueness theorems. The uniqueness theorem of §2 generalizes results obtained earlier by the author , .
Existence and uniqueness theorems. Let B be the (n+1)-dimensional region given by () and let B' be the subregion of B.
Abstract. In some physical problems (mechanical problems, optimal control problems, phase transition problems, etc.), we have to minimize a functionalJ over a topological space U for whichJ is not sequentially lower semicontinuous. In this article, we prove new existence results for general one-dimensional vector problems of calculus of variations without any convexity condition on the Cited by: This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier–Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier–Stokes equations.
() Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method.
Nonlinear Cited by: Abstract. The existence and uniqueness of the -generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
1. Introduction. The singularity of solution for boundary value problems to two-dimensional Cited by: 1.THEOREM 2 EXISTENCE AND UNIQUENESS THEOREM 1. A linear system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column, that is, if and only if an echelon form of the augmented matrix has no row of the form 0b, with b 6D0.
2. If a linear system is consistent, then the solution set con-tains eitherFile Size: 29KB.